# Inverse design optimization framework via a two-step deep learning approach: application to a wind turbine airfoil

arXiv: https://arxiv.org/abs/2108.08500 · HTML: https://mlsanity.com/paper/2108.08500/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 59 references that are in the map.
- First posted on arXiv 19 Aug 2021.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [pymoo: Multi-objective Optimization in Python](https://mlsanity.com/paper/2002.04504/) (2020)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Airfoil Design Parameterization and Optimization using B'ezier Generative Adversarial Networks](https://mlsanity.com/paper/2006.12496/) (2020)
- [Enhanced data efficiency using deep neural networks and Gaussian processes for aerodynamic design optimization](https://mlsanity.com/paper/2008.06731/) (2020)
- [Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation](https://mlsanity.com/paper/2101.02744/) (2021)

## Built on by (most cited first, 14 of 14)

- [Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder](https://mlsanity.com/paper/2205.00608/) (2022)
- [Data-Driven Physics-Informed Neural Networks: A Digital Twin Perspective](https://mlsanity.com/paper/2401.08667/) (2024)
- [Design Space Exploration and Explanation via Conditional Variational Autoencoders in Meta-model-based Conceptual Design of Pedestrian Bridges](https://mlsanity.com/paper/2211.16406/) (2022)
- [Data-Efficient Deep Operator Network for Unsteady Flow: A Multi-Fidelity Approach with Physics-Guided Subsampling](https://mlsanity.com/paper/2503.17941/) (2025)
- [Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction](https://mlsanity.com/paper/2406.03789/) (2024)
- [Towards Reliable Uncertainty Quantification via Deep Ensembles in Multi-output Regression Task](https://mlsanity.com/paper/2303.16210/) (2023)
- [How well do generative models solve inverse problems? A benchmark study](https://mlsanity.com/paper/2601.23238/) (2026)
- [Generative method for aerodynamic optimization based on classifier-free guided denoising diffusion probabilistic model](https://mlsanity.com/paper/2503.07056/) (2025)
- [Generative Design of Ship Propellers using Conditional Flow Matching](https://mlsanity.com/paper/2601.21637/) (2026)
- [Compact and Intuitive Airfoil Parameterization Method through Physics-aware Variational Autoencoder](https://mlsanity.com/paper/2311.10921/) (2023)
- [Learning with Geometry: Including Riemannian Geometric Features in Coefficient of Pressure Prediction on Aircraft Wings](https://mlsanity.com/paper/2401.09452/) (2023)
- [Neural surrogates for designing gravitational wave detectors](https://mlsanity.com/paper/2511.19364/) (2025)
- [Physics-Informed Uncertainty Enables Reliable AI-driven Design](https://mlsanity.com/paper/2601.18638/) (2026)
- [A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design](https://mlsanity.com/paper/2605.11759/) (2026)

## Abstract (arXiv)

The inverse approach is computationally efficient in aerodynamic design as the desired target performance distribution is prespecified. However, it has some significant limitations that prevent it from achieving full efficiency. First, the iterative procedure should be repeated whenever the specified target distribution changes. Target distribution optimization can be performed to clarify the ambiguity in specifying this distribution, but several additional problems arise in this process such as loss of the representation capacity due to parameterization of the distribution, excessive constraints for a realistic distribution, inaccuracy of quantities of interest due to theoretical/empirical predictions, and the impossibility of explicitly imposing geometric constraints. To deal with these issues, a novel inverse design optimization framework with a two-step deep learning approach is proposed. A variational autoencoder and multi-layer perceptron are used to generate a realistic target distribution and predict the quantities of interest and shape parameters from the generated distribution, respectively. Then, target distribution optimization is performed as the inverse design optimization. The proposed framework applies active learning and transfer learning techniques to improve accuracy and efficiency. Finally, the framework is validated through aerodynamic shape optimizations of the wind turbine airfoil. Their results show that this framework is accurate, efficient, and flexible to be applied to other inverse design engineering applications.